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Functional Characterization of Oscillatory and Excitable Media

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Abstract

Cardiac and neural systems share common features of intrinsic oscillation in some cells as well as the ability to propagate excitation. One theoretical approach to study such systems is to develop realistic models for the tissue. This involves first developing detailed ionic “Hodgkin–Huxley”-type models of individual cells and then connecting the individual cells via synaptic and gap junctions in realistic geometries. An alternative approach is to characterize tissue in terms of functional properties such as phase resetting curves and restitution curves. Using simple models based on one-dimensional difference equations, the measured functional curves can be used to predict, analyze, and interpret nonlinear dynamical phenomena. This approach offers the prospects of providing simplified descriptions that offer insight into the experimental and clinical cardiac dynamics.

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Notes

  1. Neuroscience papers generally use the term Type 1, but since we have used “Type” to characterize topology, we use “Class” to distinguish unimodal and bimodal resetting curves.

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Acknowledgments

We thank NSERC, the Canadian Heart and Stroke Foundation, and CIHR for financial support. We thank M. R. Guevara for helpful comments, and also for the insightful contributions he made to the development of the ideas presented here.

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  1. Department of Physiology, McGill University, 3655 Promenade Sir William Osler, Montreal, QC , H3G 1Y6, Canada

    Leon Glass & Alvin Shrier

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  1. Leon Glass
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Correspondence to Leon Glass.

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Glass, L., Shrier, A. Functional Characterization of Oscillatory and Excitable Media. Bull Math Biol 77, 782–795 (2015). https://doi.org/10.1007/s11538-014-0015-y

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